How to find the solution x of 2\sin11^\circ\sin71^\circ\sin(x^\circ+30^\circ)=\sin2013^\circ\sin210^\circ

leciazyg

leciazyg

Answered question

2022-02-27

How to find the solution x of 2sin11sin71sin(x+30)=sin2013sin210

Answer & Explanation

King Osborn

King Osborn

Beginner2022-02-28Added 6 answers

You've over complicated the whole thing way too much. Don't forget, apart from sin(x+30), the rest are just constants and so treat them like any other number. Therefore you can just do the whole thing simply and like normal:
2sin(11)sin(71)sin(x+30)=sin(2013)sin(210)
=2sin(11)sin(71)sin(x+30)=sin(33)sin(30)
as they're all multiplied, divide through by the 2sin(11)sin(71) to get
sin(x+30)=sin(33)sin(30)2sin(11)sin(71)
Then arcsin both sides to get
x+30=sin1(sin(33)sin(30)2sin(11)sin(71))=49
Subtracting 30 then gives you x=19 and as you want it in the interval 90<x<180, you simply do 90+19=109

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